Simplify the following expression: $k = \dfrac{36x - 84}{-108x + 48}$ You can assume $x \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $36x - 84 = (2\cdot2\cdot3\cdot3 \cdot x) - (2\cdot2\cdot3\cdot7)$ The denominator can be factored: $-108x + 48 = - (2\cdot2\cdot3\cdot3\cdot3 \cdot x) + (2\cdot2\cdot2\cdot2\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $k = \dfrac{(12)(3x - 7)}{(12)(-9x + 4)}$ Dividing both the numerator and denominator by $12$ gives: $k = \dfrac{3x - 7}{-9x + 4}$